Answer the following two questions and justify your answers:
(1) What is the last digit of the sum 1^{2012}+2^{2012}+3^{2012}+4^{2012}+5^{2012}?
(2) What is the last digit of the sum 1^{2012}+2^{2012}+3^{2012}+4^{2012}+\cdots+2011^{2012}+2012^{2012}?